Suppose you’re thinking about buying a used car, but you’ve become worried about the selection problems. In this market, the seller of each car knows the true value, but the buyer can’t determine the value until after purchase. Assume that there are 6 sellers with cars of value {$0, 1000, 2000, 3000, 4000, 5000}. (12 points)

a.What is the average value of a used car on the market?
Average value of used car = $(0 + 1000 + 2000 + 3000 + 4000 + 5000)/6 = $2500

b.If the buyer knows the average value of cars on the market, but not the actual value of any car, what is the most the buyer will pay?
$2500
c.Given what the buyer is willing to pay, which sellers will be willing to sell?
Sellers 1, 2 and 3, who have used cars that are valued at $0, $1000 and $2000.

d.Now consider the iterative (repeat the above process) behavior of buyers and sellers. If the sellers with higher valued cars than what buyers are willing to pay have left the market, now: Hint: The answers to 3b and 3d cannot be the same.
i. What is the most a buyer will be willing to pay?

ii. Which sellers will be willing to sell?
iii. What has happened to this market?

d.i. The most a buyer will be willing to pay is now the average value of the remaining cars on the market. In this case, the remaining cars are valued at $0, $1000, and $2000. So, the average value is $(0 + 1000 + 2000)/3 = $1000.

d.ii. The sellers who will be willing to sell are those with cars valued at or below $1000. In this case, only Seller 1, who has a car valued at $0, will be willing to sell.

d.iii. By iteratively removing sellers with higher valued cars from the market, the market has narrowed down to only sellers with lower valued cars. The market has become more restricted and limited to sellers with cars that are valued below or equal to the buyer's willingness to pay.

i. The most a buyer will be willing to pay is now the average value of the remaining cars on the market.

In this case, let's assume that the sellers with cars valued at $4000 and $5000 have left the market. Therefore, the average value of the remaining cars is $(0 + 1000 + 2000 + 3000)/4 = $1500.

So, the most a buyer will be willing to pay is $1500.

ii. The sellers who will be willing to sell are the ones with cars valued at or below the most the buyer is willing to pay.

In this case, the sellers with cars valued at $0, $1000, and $2000 will still be willing to sell.

iii. This market has seen a decrease in the average value of cars and the sellers with higher-valued cars have left the market, leaving only the lower-valued cars available for sale. This is a normal outcome in the used car market where buyers have limited information and sellers adjust their prices accordingly based on buyer behavior.